I recently learned that Aerolineas Argentinas was a fairly major Comet 4 operator - I already knew about Mexicanas' Comets and CP's cancelled order: did any other airlines in the Americas/W. Hemisphere operate Comets?
Also, who had a bigger fleet, MX or AR?
Who got theirs first?
Who kept them longest?
What routes did MX and AR use them on?

None as far as I know.
Capitol, a big Vickers Viscount customer, ordered 14 Comet 4's in the late 50's, but after financial issues and eventual merger with I think UA, the order was cancelled before anything came down the production line.

AR operated Comets first with LV PLM (c/n 6418) delivered in early 1959. Half a dozen aircraft were delivered within a couple of years, and a further one in 1962. Three aircraft were written off between August 59 and November 61.

MX operated Comets purchased new (delivered from 1960) and also some purchased secondhand from BOAC.AFAIK, no MX aircraft were written off.

Both airlines had sold their Comet fleets by the end of 1971

If we're discussing Comets in the Americas, there were of course a number of other aircraft registered in USA too.

MX was the launch customer of the DH Comet 4C in 1960. This was discussed a while ago in:MX Launch Customer Of DH Comet 4C(by Adriaticus Jul 18 2004 in Civil Aviation)
this thread includes some nice and interesting photographs, like